Logic Metapuzzle Generator

This Demonstration provides another generator of knights and knaves logic puzzles. These puzzles are about an island in which some natives called "knights" always tell the truth and other natives called "knaves" always lie. Assume that every native is either a knight or a knave.
In the problem there are natives, A, B, C, …, each of whom makes a statement about the number of knights in a set. They know the empty set { } with no knights. Their vocabulary is rather limited; they only talk about even {0, 2, 4, …} and odd {1, 3, 5, …} numbers.
The statement of the last native was not recorded properly, but a logician who had heard the statement was able to infer who was a knight and who was a knave. Can you infer who is a knight and who is a knave?

SNAPSHOTS

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DETAILS

These kinds of logic puzzles are called "metapuzzles" [2].
References
[1] R. M. Smullyan, What Is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles, Englewood Cliffs, NJ: Prentice–Hall, 1978.
[2] R. M. Smullyan, The Lady or the Tiger? And Other Logic Puzzles, New York: Alfred A. Knopf, 1983, p. 91.
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